By Guoliang Wang, Qingling Zhang, Xinggang Yan

ISBN-10: 3319087223

ISBN-13: 9783319087221

ISBN-10: 3319087231

ISBN-13: 9783319087238

This monograph is an updated presentation of the research and layout of singular Markovian leap platforms (SMJSs) during which the transition expense matrix of the underlying platforms is usually doubtful, in part unknown and designed. the issues addressed contain balance, stabilization, H∞ regulate and filtering, observer layout, and adaptive regulate. functions of Markov procedure are investigated through the use of Lyapunov concept, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, between different techniques.

Features of the booklet include:

· learn of the steadiness challenge for SMJSs with common transition cost matrices (TRMs);

· stabilization for SMJSs via TRM layout, noise regulate, proportional-derivative and partly mode-dependent keep an eye on, when it comes to LMIs with and with out equation constraints;

· mode-dependent and mode-independent H∞ keep watch over ideas with improvement of one of those disordered controller;

· observer-based controllers of SMJSs during which either the designed observer and controller are both mode-dependent or mode-independent;

· attention of strong H∞ filtering when it comes to doubtful TRM or filter out parameters resulting in a mode for completely mode-independent filtering

· improvement of LMI-based stipulations for a category of adaptive kingdom suggestions controllers with almost-certainly-bounded expected mistakes and almost-certainly-asymptotically-stable corresponding closed-loop method states

· functions of Markov strategy on singular structures with norm bounded uncertainties and time-varying delays

*Analysis and layout of Singular Markovian bounce Systems* comprises precious reference fabric for educational researchers wishing to discover the world. The contents also are compatible for a one-semester graduate course.

**Read Online or Download Analysis and Design of Singular Markovian Jump Systems PDF**

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**Additional info for Analysis and Design of Singular Markovian Jump Systems**

**Example text**

22) where ⎢ ⎣ ≤ ≤ ≤ ≤ Δˆ i2 = πi1 PiT , . . , πi(i−1) PiT πi(i+1) PiT , . . , πi N PiT , Δˆ i3 = −diag{(P1 )Π − ε1 I, . . , (Pi−1 )Π − εi−1 I, (Pi+1 )Π − εi+1 I, . . , (PN )Π − ε N I }. 2 Robust Stabilization 57 Then, the corresponding gain is given as K i = Yi Pi−1 . 1). 25) where ⎢ ⎣ ≤ ≤ ≤ ≤ Δˇ i2 = πi1 X iT , . . , πi(i−1) X iT πi(i+1) X iT , . . , πi N X iT , ⎣ ⎢ ≤ ≤ ≤ ≤ Δˆ i3 = πi1 X iT E T , . . , πi(i−1) X iT E T πi(i+1) X iT E T , . . , πi N X iT E T , Δi4 = −4diag{ε1 I, . . , εi−1 I, εi+1 I, .

IEEE Trans Autom Control 56:858–863 27. Lu GP, Ho DWC (2006) Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation. IEEE Trans Autom Control 51:813–823 28. Gao YB, Lu GP, Wang ZM (2010) Passivity analysis of uncertain singularly perturbed systems. IEEE Trans Circuits Syst ii Express Briefs 57:486–490 29. Shao ZH (2004) Robust stability of two-time-scale systesm with nonlinear uncertainties. IEEE Trans Automaic Control 49:258–261 30. Nguang SK, Assawinchaichote W, Shi P (2007) Robust H⊆ control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach.

X N )Π − ε N I }. 10). 4 [5] Let μi be a given scalar. 26) where ⎢ ⎣Π ⎢ ⎣ + πii μi (E X i )Π − μi2 E Pˆi E T , X i = Pˆi E T + V Qˆ i U, Δ˜ i1 = Ai X i + Bi L i E T + Hi V T ⎣ ⎢ ≤ ≤ ≤ ≤ Δ˜ i2 = πi1 X iT E R , . . , πi(i−1) X iT E R πi(i+1) X iT E R , . . , πi N X iT E R . 6), some additional inequalities are introduced or some parameters are given beforehand. 1, a corollary could be obtained directly, in which no more inequalities are used and no parameters are given in advance.

### Analysis and Design of Singular Markovian Jump Systems by Guoliang Wang, Qingling Zhang, Xinggang Yan

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